0
Research Papers

Irregular Inhomogeneities in an Anisotropic Piezoelectric Plane

[+] Author and Article Information
L. G. Sun

Department of Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering,  Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

K. Y. Xu1

Department of Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering,  Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chinakyxu@shu.edu.cn

E. Pan

The School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, China; Department of Civil Engineering,  The University of Akron, Akron, OH 44325-3905pan2@uakron.edu

1

Corresponding author.

J. Appl. Mech 79(2), 021014 (Feb 24, 2012) (10 pages) doi:10.1115/1.4005557 History: Received December 29, 2010; Revised August 30, 2011; Posted January 31, 2012; Published February 13, 2012; Online February 24, 2012

This paper presents an analytical solution for the Eshelby problem of polygonal inhomogeneity in an anisotropic piezoelectric plane. By virtue of the equivalent body-force concept of eigenstrain, the induced elastic and piezoelectric fields in the corresponding inclusion are first expressed in terms of the line integral along its boundary with the integrand being the Green’s functions, which is carried out analytically. The Eshelby inhomogeneity relation for the elliptical shape is then extended to the polygonal inhomogeneity, with the final induced field involving only elementary functions with small steps of iteration. Numerical solutions are compared to the results obtained from other methods, which verified the accuracy of the proposed method. Finally, the solution is applied to a triangular and a rectangular quantum wire made of InAs within the semiconductor GaAs full-plane substrate.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

A general polygonal inhomogeneity problem in an anisotropic piezoelectric plane: An extended eigenstrain γIjp(γijp-Ejp) within an arbitrarily shaped polygon. The material properties within and outside the polygon are CiJLm* and CiJLm, respectively. If CiJLm* equal to CiJLm, the inhomogeneity problem is then reduced to the inclusion problem.

Grahic Jump Location
Figure 2

(a) A triangular QWR (SiC) in an isotropic elastic full-plane under a far-field stress σ0 (Young modulus = 210 GPa, Poisson’s ratio = 0.3). (b) Stress σzz along the x-axis.

Grahic Jump Location
Figure 3

(a) A triangular QWR (Ti-6Al-4V) in an isotropic elastic full-plane under a far-field stress σ0 (Young modulus = 210 GPa, Poisson’s ratio = 0.3). (b) Stress σzz along the x-axis.

Grahic Jump Location
Figure 4

(a) A rectangular QWR (ZrO2 ) in an isotropic elastic Al2 O3 full-plane under a far-field stress σ0 . (b) Stress σzz/σ0 along the x-axis.

Grahic Jump Location
Figure 5

(a) Triangular QWR of InAs (001) within the GaAs (001) full plane (under a hydrostatic eigenstrain in QWR). (b) Stress σxx along the x-axis. (c) Stress σxx along the z-axis. (d) Stress σzz along the x-axis. (e) Stress σzz along the z-axis. (f) Stress σxz along the z-axis. (g) Electric displacement Dz along the z-axis.

Grahic Jump Location
Figure 6

(a) Triangular QWR of InAs (111) within the GaAs (111) full plane (under a hydrostatic eigenstrain in QWR). (b) Stress σxx along the x-axis. (c) Stress σxx along the z-axis. (d) Stress σzz along the x-axis. (e) Stress σzz along the z-axis. (f) Stress σxz along the z-axis. (g) Electric displacement Dx along the x-axis. (h) Electric displacement Dx along the z-axis.

Grahic Jump Location
Figure 7

(a) Rectangular QWR of InAs (001) within the GaAs (001) full plane (under a hydrostatic eigenstrain in QWR). (b) Stress σxx along the x-axis. (c) Stress σxx along the z-axis. (d) Stress σzz along the x-axis. (e) Stress σzz along the z-axis.

Grahic Jump Location
Figure 8

(a) Rectangular QWR of InAs (111) within the GaAs (111) full plane (under a hydrostatic eigenstrain in QWR). (b) Stress σxx along the x-axis. (c) Stress σxx along the z-axis. (d) Stress σzz along the x-axis. (e) Stress σzz along the z-axis. (f) Electric displacement Dx along the z-axis.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In